Theoretical Chemistry Accounts

, Volume 115, Issue 5, pp 370–378 | Cite as

Information Theory, the Shape Function, and the Hirshfeld Atom

  • Paul W. AyersEmail author
Regular Article


Following the work of Nalewajski and Parr, there has been a surge of interest in the use of information theory to describe chemical bonding and chemical reactions. However, the measure of “information” used by Nalewajski and Parr is not any of the usual conventional entropies, chiefly because the electron density is not normalized to one. The consequences of this are discussed, and a solution is constructed using the shape function and an “entropy of mixing” term. The same revision, however, cannot be made when if the Tsallis entropy, instead of the Shannon form, is used. This serves to emphasize that the Hirshfeld atom is a very specific result, associated only with logarithmic measures of information. A less specific derivation due to Nalewajski provides one resolution to this quandary; this derivation is analyzed in detail.


Entropy Shape Function Chem Phys Fisher Information Directed Divergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of ChemistryMcMaster UniversityHamiltonCanada

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